Staal scored 44 seconds into the first period to give the Hurricanes a 1-0 lead, redirecting Jalen Chatfield's shot in front.
Jesper Fast made it 2-0 at 3:52 when he finished a backhand pass from Staal near the left post on a 2-on-1.
"We were smart with the puck and made the right plays," Staal said. "We have trust in our game."
Following the goal, Lambert called a timeout, and Holmstrom responded to cut it to 2-1 at 14:02. He skated into the high slot, pulled the puck back, and shot blocker side on Andersen through the legs of Brett Pesce.
Nelson tied it 2-2 at 15:42 with a wraparound that went into the net off the stick of Teuvo Teravainen.
"It's a good job of responding," Nelson said. "A huge goal by Simon, and then the difference is you'd like to follow it up and get the next one to get the lead and keep rolling with the momentum.
"They're a tough team to play. Their 'D' are tight on [you]. There's not a lot of space. … It's just a tough game. It didn't feel like we had a ton of looks to maybe get that one, and that's the difference."